Is it possible to paint an object inside with one texture and outside with another?
So, as your question is equivocal, you have 2 possible situations: Either you're talking about an object that is open and you need to give 2 different materials to each side of the same face OR you're talking about the intersection of an object with its boolean object.


Option 1: For an open mesh, use the Geometry > Backfacing node as you explain. Mix it in a Mix shader to separate 2 different shaders.





Option 2, if you're talking about the face that is the intersection between your tooth and the object you'll use as boolean, you need to give your boolean object the material you want to see, and make sure that your tooth has both its natural material + the same material as its boolean object. Here, both the cube and the tooth have the orange material: